Several procedures have been proposed and developed to overcome the challenge in ultradeepwaters testing. A realistic alternative approach uses a hybrid passive methodology through equivalent truncated mooring systems. Often, the searching for equivalent systems involves using a trial-and-error. As an alternative, researches on the use of optimization techniques to establish truncated mooring system with the required properties have been attempted in recent years. In the literature, it is available only approaches considering nongradient-based algorithms. These algorithms usually involve several parameters which require appropriate tuning to provide good performance. Our approach involves optimization algorithms based on gradient. We use a calibration method to perform a static adjustment of design variables to optimally fit truncated mooring system to full-depth mooring system, which proved efficient. A further feature of this work is related to the study of the influence of design variables on the response, through a methodology based on design of experiments (DOE), avoiding the use of irrelevant variables. It should be emphasized that to the authors' knowledge this DOE methodology presented was not seen in other works in this field. We will show that the methodology proposed in this work makes easy to find an equivalent mooring system on truncated water depth. We will present and discuss two fictitious cases, one case based on the literature and another case based on a real scenario. The results show a good agreement between truncated mooring system and full-depth mooring system for the static adjustment.

References

References
1.
Chakrabarti
,
S.
,
2005
,
Handbook of Offshore Engineering
(Elsevier Ocean Engineering Series),
Elsevier
,
London
, Chap. 13.
2.
Buchner
,
B.
,
1999
, “
Model Test Challenges for Deep Water Floaters
,”
14th Annual Conference on Floating Production Systems
, (
FPS
), London, Dec. 2–3.
3.
Stansberg
,
C. T.
,
Karlsen
,
S. I.
,
Ward
,
E. G.
,
Wichers
,
J. E. W.
, and
Irani
,
M. B.
,
2004
, “
Model Testing for Ultradeep Waters
,”
Offshore Technology Conference
(OTC), Houston, TX, May 3–6, Vol. 2,
SPE
Paper No. OTC-16587-MS.
4.
Stansberg
,
C. T.
,
Ormberg
,
H.
, and
Oritsland
,
O.
,
2002
, “
Challenges in Deep Water Experiments: Hybrid Approach
,”
ASME J. Offshore Mech. Arct. Eng.
,
124
(
2
), pp.
90
96
.
5.
Dercksen
,
A.
, and
Wichers
,
J. E. W.
,
1992
, “
A Discrete Element Method on a Chain Turret Tanker Exposed to Survival Conditions
,” 6th International Conference on the Behaviour of Offshore Structures (
BOSS92
), London, July 7–10, Vol.
1
, pp.
238
250
.
6.
Kim
,
M. H.
,
Ran
,
Z.
,
Zheng
,
W.
,
Bhat
,
S.
, and
Beynet
,
P.
,
1999
, “
Hull/Mooring Coupled Dynamic Analysis of a Truss Spar in Time Domain
,” The Ninth International Offshore and Polar Engineering Conference (ISOPE), Brest, France, May 30–June 4,
SPE
Paper No. ISOPE-01-11-1-042.
7.
Chen
,
X.
,
Zhang
,
J.
,
Johnson
,
P.
, and
Irani
,
M.
,
2000
, “
Studies on the Dynamics of Truncated Mooring Line
,” The Tenth International Offshore and Polar Engineering Conference (ISOPE), Seattle, WA, May 28–June 2,
SPE
Paper No. ISOPE-I-00-126.
8.
Stansberg
,
C. T.
,
Yttervik
,
R.
,
Oritsland
,
O.
, and
Kleiven
,
G.
,
2000
, “
Hydrodynamic Model Test Verification of a Floating Platform System in 3000 m Water Depth
,” Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering (
OMAE
), New Orleans, LA, Feb. 14–17, pp. 325–334.
9.
Zhang
,
H.
,
Sun
,
Z.
,
Yang
,
J.
, and
Gao
,
M.
,
2009
, “
Investigation on Optimization Design of Equivalent Water Depth Truncated Mooring System
,”
Sci. China Ser. G: Phys. Mech. Astron.
,
52
(
2
), pp.
277
292
.
10.
Zhang
,
H.
,
Gao
,
W.
,
Wang
,
Q.
,
Jiang
,
J.
, and
Zhao
,
Z.
,
2012
, “
Investigation on Optimization Design of an Equivalent Water Depth Truncated Mooring System Based on INSGA-II
,”
J. Mar. Sci. Appl.
,
11
(
2
), pp.
208
215
.
11.
Zhang
,
H.
,
Huang
,
S.
, and
Guan
,
W.
,
2014
, “
Optimal Design of Equivalent Water Depth Truncated Mooring System Based on Baton Pattern Simulated Annealing Algorithm
,”
China Ocean Eng.
,
28
(
1
), pp.
67
80
.
12.
Wang
,
H.
,
Ma
,
G.
,
Sun
,
L.
, and
Kang
,
Z.
,
2016
, “
Truncation Design and Model Testing of a Deepwater FPSO Mooring System
,”
ASME J. Offshore Mech. Arct. Eng.
,
138
(
2
), p.
021603
.
13.
Fylling
,
I. J.
, and
Stansberg
,
C. T.
,
2005
, “
Model Testing of Deepwater Floating Production Systems: Strategy for Truncation of Moorings and Risers
,”
17th Deep Oil Technology Conference
(
DOT
), Rio de Janeiro, Brazil, pp.
1
4
.
14.
Fan
,
T.
,
Qiao
,
D.
, and
Ou
,
J.
,
2012
, “
Optimized Design of Equivalent Truncated Mooring System Based on Similarity of Static and Damping Characteristics
,”
22nd International Offshore and Polar Engineering Conference
(ISOPE), Rhodes, Greece, June 17–23,
SPE
Paper No. ISOPE-I-12-137.
15.
Molins
,
C.
,
Trubat
,
P.
,
Gironella
,
X.
, and
Campos
,
A.
,
2015
, “
Design Optimization for a Truncated Catenary Mooring System for Scale Model Test
,”
J. Mar. Sci. Eng.
,
3
(
4
), pp.
1362
1381
.
16.
Felix-Gonzalez
,
I.
, and
Mercier
,
R. S.
,
2016
, “
Optimized Design of Statically Equivalent Mooring Systems
,”
Ocean Eng.
,
111
, pp.
384
397
.
17.
Waals
,
O. J.
, and
van Dijk
,
R. R. T.
,
2004
, “
Truncation Methods for Deep Water Mooring Systems for a Catenary Moored FPSO and a Semi Taut Moored Semi Submersible
,”
Deep Offshore Technology Conference
(
DOT
), New Orleans, LA, Nov. 30–Dec. 2, Paper No. 24-1.
18.
Ferreira
,
F. M. G.
,
Lages
,
E. N.
,
Afonso
,
S. M. B.
, and
Lyra
,
P. R. M.
,
2016
, “
Dynamic Design Optimization of an Equivalent Truncated Mooring System
,”
Ocean Eng.
,
122
, pp.
186
201
.
19.
Gill
,
P. E.
,
Murray
,
W.
, and
Wright
,
M. H.
,
1981
,
Practical Optimization
, Vol.
5
,
Academic Press
,
London
, Chap. 4.
20.
Nishimoto
,
K.
,
Fucatu
,
C. H.
, and
Masetti
,
I. Q.
,
2002
, “
Dynasim—A Time Domain Simulator of Anchored FPSO
,”
ASME J. Offshore Mech. Arct. Eng.
,
124
(
4
), pp.
203
211
.
21.
Silveira
,
E. S. S.
,
Lages
,
E. N.
, and
Ferreira
,
F. M. G.
,
2012
, “
DOOLINES: An Object-Oriented Framework for Non-Linear Static and Dynamic Analyses of Offshore Lines
,”
Eng. Comput.
,
28
(
2
), pp.
149
159
.
22.
Adams
,
B. M.
,
Bauman
,
L. E.
,
Bohnhoff
,
W. J.
,
Dalbey
,
K. R.
,
Ebeida
,
M. S.
,
Eddy
,
J. P.
,
Eldred
,
M. S.
,
Hough
,
P. D.
,
Hu
,
K. T.
,
Jakeman
,
J. D.
,
Swiler
,
L. P.
, and
Vigil
,
D. M.
,
2009
, “
DAKOTA, a Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 5.4 User's Manual
,” Sandia National Laboratories, Albuquerque, NM, Report No.
SAND2010-2183
.
23.
Ji
,
C.
, and
Xu
,
S.
,
2014
, “
Verification of a Hybrid Model Test Method for a Deep Water Floating System With Large Truncation Factor
,”
Ocean Eng.
,
92
, pp.
245
254
.
24.
Telford
,
J. K.
,
2007
, “
A Brief Introduction to Design of Experiments
,”
Johns Hopkins APL Tech. Dig.
,
27
(3), pp.
224
232
.
25.
Martins
,
M. A. L.
,
Lages
,
E. N.
, and
Silveira
,
E. S. S.
,
2013
, “
Compliant Vertical Access Riser Assessment: DOE Analysis and Dynamic Response Optimization
,”
Appl. Ocean Res.
,
41
, pp.
28
40
.
26.
Islam
,
M. F.
, and
Lye
,
L.
,
2009
, “
Combined Use of Dimensional Analysis and Modern Experimental Design Methodologies in Hydrodynamics Experiments
,”
Ocean Eng.
,
36
(
3
), pp.
237
247
.
27.
Kim
,
J.-H.
,
Lee
,
H.-C.
,
Kim
,
J.-H.
,
Choi
,
Y.-S.
,
Yoon
,
J.-Y.
,
Yoo
,
I.-S.
, and
Choi
,
W.-C.
,
2015
, “
Improvement of Hydrodynamic Performance of a Multiphase Pump Using Design of Experiment Techniques
,”
ASME J. Fluids Eng.
,
137
(
8
), p.
081301
.
28.
Lee
,
S. E.
,
Paik
,
J. K.
,
Ha
,
Y. C.
,
Kim
,
B. J.
, and
Seo
,
J. K.
,
2014
, “
An Efficient Design Methodology for Subsea Manifold Piping Systems Based on Parametric Studies
,”
Ocean Eng.
,
84
, pp.
273
282
.
29.
Bouchekara
,
H. R. E.
,
Anwari
,
M.
, and
Simsim
,
M.
,
2012
, “
Optimization of Induction Motors Using Design of Experiments and Particle Swarm Optimization
,”
Induction Motors—Modelling and Control
,
R. E.
Araújo
, ed.,
InTech
, Rijeka, Croatia, Chap. 7.
30.
Cavazzuti
,
M.
,
2012
,
Optimization Methods: From Theory to Design Scientific and Technological Aspects in Mechanics
,
Springer
,
Berlin
, Chap. 2.
31.
Montgomery
,
D. C.
,
2000
,
Design and Analysis of Experiments
,
Wiley
,
New York
, Chap. 8.
32.
Adams
,
B. M.
,
Swiler
,
L. P.
,
Hooper
,
R.
,
Lewis
,
A.
,
McMahan
,
J. A.
,
Smith
,
R. C.
, and
Williams
,
B. J.
,
2014
, “
User Guidelines and Best Practices for CASL VUQ Analysis Using Dakota
,” Sandia National Laboratories, Albuquerque, NM, Technical Report No.
CASL-U-2014-0038-000
.
33.
Dennis
,
J. E.
, Jr.
,
Gay
,
D. M.
, and
Welsch
,
R. E.
,
1981
, “
Algorithm 573: NL2SOL—An Adaptive Nonlinear Least-Squares Algorithm [E4]
,”
ACM Trans. Math. Software
,
7
(
3
), pp.
369
383
.
34.
Gay
,
D. M.
,
1990
, “
Usage Summary for Selected Optimization Routines
,” AT&T Bell Laboratories, Murray Hill, NJ, Technical Report No.
153
.
35.
Schwartz
,
R. L.
, and
Christiansen
,
T.
,
1996
,
Programming Perl
,
O'Reilly Media, Inc.
,
Sebastopol, CA
, Chap. 1.
36.
Collette
,
Y.
, and
Siarry
,
P.
,
2013
,
Multiobjective Optimization: Principles and Case Studies
,
Springer Science & Business Media
,
Berlin
, Chap. 1.
37.
Motta
,
R. S.
,
Afonso
,
S. M. B.
, and
Lyra
,
P. R. M.
,
2012
, “
A Modified NBI and NC Method for the Solution of N-Multiobjective Optimization Problems
,”
Struct. Multidiscip. Optim.
,
46
(
2
), pp.
239
259
.
38.
Anthony
,
D. K.
,
Elliott
,
S. J.
, and
Keane
,
A. J.
,
2000
, “
Robustness of Optimal Design Solutions to Reduce Vibration Transmission in a Lightweight 2-D Structure, Part I: Geometric Design
,”
J. Sound Vib.
,
229
(
3
), pp.
505
528
.
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